Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

Cora Diamond has recently criticised as mere legend the interpretation of a quip of Ramsey's, contained in the epigraph below, which takes him to be objecting to or rejecting Wittgenstein's Tractarian distinction between saying and showing. Whilst I agree with Diamond's discussion of the legend, I argue that her interpretation of the quip has little evidential support, and runs foul of a criticism sometimes made against intuitionism. Rather than seeing Ramsey as making a claim about the nature of propositions, as (...) Diamond does, we should understand him as making a claim about the grammar of the logical connectives. Such a view coheres with the extant evidence of the nature of Wittgenstein's and Ramsey's 1929 philosophical encounters. It is also compatible with attributing to Ramsey a recognition of Wittgenstein's distinction and with denying that criticising it is the lesson of the quip. (shrink)

There is, in the Ramsey Archive at the Hillman Library of the University of Pittsburgh, a note, written in 1929, in Ramsey's hand and mostly in German, consisting of twenty paragraphs the contents...

Frank Plumpton Ramsey was born in February 1903, and he died in January 1930—just before his 27th birthday. In his short life he produced an extraordinary amount of profound and original work in economics, mathematics and logic as well as in philosophy: work which in all these fields is still, over sixty years on, extremely influential.

In this paper, I examine the transmission of some ideas of the pragmatist tradition to Wittgenstein, in his ‘middle period,’ through the intermediary of F. P. Ramsey, with whom he had numerous fruitful discussions at Cambridge in 1929. I argue more specifically that one must first come to terms with Ramsey’s own views in 1929, and explain how they differ from views expressed in earlier papers from 1925-27, so a large part of this paper is devoted to this task. One (...) is then in a better position to understand the impact of Ramsey’s astute critique of Wittgenstein’s Tractatus Logico-Philosophicus in conjunction with his pragmatism, and explain how it may have set into motion the ‘later’ Wittgenstein. I then argue that Ramsey introduced his notion of ‘variable hypothetical’ as a rule, not a proposition, on pragmatist grounds and that Wittgenstein picked this up in 1929, along with a more ‘dynamic’ view of meaning than the ‘static’ view of the Tractatus, and that this explains in part Wittgenstein’s turn to his ‘later philosophy.’. (shrink)

Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...) in the foundational controversy of the 1920s. In addition, they reveal Weyl's hitherto unknown objections to Becker's detailed attempt (Mathematische Existenz, 1927) to ground the transfinite phenomenologically. (shrink)

In 'General Propositions and Causality' Ramsey rejects his earlier view that universal generalizations are infinite conjunctions, arguing that they are not genuine propositions at all. We argue that his new position is unstable. The issues about infinity that lead Ramsey to the new view are essentially those underlying Wittgenstein's rule-following considerations. If they show that generalizations are not genuine propositions, they show that there are no genuine propositions. The connection raises interesting historical questions about the direction of influence between Ramsey (...) and Wittgenstein, the origin of the rule-following argument, and the influence of writers such as Brouwer. (shrink)

Frank Plumpton Ramsey was born in February 1903, and he died in January 1930—just before his 27th birthday. In his short life he produced an extraordinary amount of profound and original work in economics, mathematics and logic as well as in philosophy: work which in all these fields is still, over sixty years on, extremely influential.

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)